1. Field of the Invention
The present invention relates generally to a multiple antenna communication system, and more particularly, to an apparatus and a method for channel encoding and decoding a codeword based on a Low-Density Parity-Check (LDPC) code applying puncturing in the multiple antenna communication system.
2. Description of the Related Art
In a communication system, noises, fading, and Inter-Symbol Interference (ISI) of a channel distort a signal being transmitted. Particularly, in high-speed digital communication systems, such as advanced mobile communication, digital broadcasting, and mobile Internet, requiring high data throughput and high reliability, it is important to overcome signal distortion caused by noise, fading, and ISI. Channel coding and interleaving are some of the techniques for overcoming signal distortion.
Specifically, interleaving is used to prevent burst errors that frequently occur during channel fading, to minimize data transmission loss, and to enhance a channel coding effect, by distributing errors of transmitted bits over multiple points.
The channel coding is often used to enhance communication reliability in that a receiving node can confirm signal distortion caused by noise, fading, and ISI, and efficiently recover the original signal. Codes used in channel coding are often referred to as “Error-Correcting Codes (ECC)”.
Conventional ECCs include a parity-check code based on a parity-check matrix. The parity-check code can be defined using a parity-check matrix or a generator matrix. Basically, the parity-check matrix H or the generator matrix G of the parity-check code is given, and a codeword is determined to satisfy a relation as shown in Equation (1).m·G=c H·cT=0  (1)
In Equation (1), m denotes an information word of a length K including K-ary information bits, and (m0, m1, . . . , mK−1). H denotes the parity-check matrix, G denotes the generator matrix, and c denotes a codeword obtained from the information word.
When the parity-check matrix is systematic, the codeword c is expressed as (m, p), where p denotes the parity. In general, when a message i.e., an information word) length is K and the codeword length is N, the parity length p is (N−K). With full rank, the size of the parity-check matrix is (N−K)×N.
As for the systematic coding, the parity-check matrix as shown in Equation (2) is possible.
                    H        =                  [                                                    1                                            0                                            0                                            0                                            1                                            0                                            0                                            1                                            0                                                                    0                                            1                                            1                                            0                                            0                                            0                                            0                                            1                                            0                                                                    0                                            1                                            0                                            0                                            0                                            1                                            0                                            0                                            1                                                                    1                                            0                                            0                                            1                                            0                                            0                                            0                                            0                                            1                                                                    1                                            0                                            1                                            1                                            0                                            0                                            1                                            0                                            0                                              ]                                    (        2        )            
In Equation (2), H denotes the parity-check matrix.
The codeword c corresponding to the parity-check matrix of Equation (2) includes the information word m=(m0, m1, m2, m3) including four information bits, and the parity p=(p0, p1, p2, p3, p4) including five parity bits. The relationship of the codeword c and the parity-check matrix H is shown in Equation (3).
                              H          ·                                    c              T                        _                          =                                            [                                                                    1                                                        0                                                        0                                                        0                                                        1                                                        0                                                        0                                                        1                                                        0                                                                                        0                                                        1                                                        1                                                        0                                                        0                                                        0                                                        0                                                        1                                                        0                                                                                        0                                                        1                                                        0                                                        0                                                        0                                                        1                                                        0                                                        0                                                        1                                                                                        1                                                        0                                                        0                                                        1                                                        0                                                        0                                                        0                                                        0                                                        1                                                                                        1                                                        0                                                        1                                                        1                                                        0                                                        0                                                        1                                                        0                                                        0                                                              ]                        ·                          [                                                                                          m                      0                                                                                                                                  m                      1                                                                                                                                  m                      2                                                                                                                                  m                      3                                                                                                                                  p                      0                                                                                                                                  p                      1                                                                                                                                  p                      2                                                                                                                                  p                      3                                                                                                                                  p                      4                                                                                  ]                                =                      0            _                                              (        3        )            
In Equation (3), H denotes the parity-check matrix, c denotes the codeword, mi denotes the information bit, and pi denotes the parity bit.
In the matrix of Equation (3), each row of the parity-check matrix represents an algebraic relational expression. Typically, an algebraic relational expression is referred to as a parity-check equation. Based on Equation (3), the algebraic relational expression is given by Equation (4).
                              [                                                                                          m                    0                                    +                                      p                    0                                    +                                      p                    3                                                                                                                                            m                    1                                    +                                      p                    2                                    +                                      p                    3                                                                                                                                            m                    1                                    +                                      p                    1                                    +                                      p                    4                                                                                                                                            m                    0                                    +                                      p                    3                                    +                                      p                    4                                                                                                                                            m                    0                                    +                                      m                    2                                    +                                                                                    m                        3                                            ++                                        ⁢                                          p                      2                                                                                                    ]                =                  [                                                    0                                                                    0                                                                    0                                                                    0                                                                    0                                              ]                                    (        4        )            
In Equation (4), mi denotes the information bit and pi denotes the parity bit.
A nonzero element in the parity-check matrix is referred to as a weight. In general, as the number of the weights increases in the parity-check code, the encoding and decoding complexity rises. That is, the fewer weights in the parity-check matrix, the lower complexity. A code with few weights is referred to as a Low-Density Parity-Check (LDPC) code. In many cases, as the codeword of the LDPC code is lengthened, the weight density lowers.
When the systematic parity-check code is applied to a space-time code, which is a type of multiple antenna system, diversity can occur according to characteristics of the parity-check matrix. The diversity improves the signal quality of each antenna stream by reducing interference between the multiple antennas. As the diversity increases, a higher data rate can be provided.
When an LDPC code is used, the maximum diversity can depend on the characteristics of the parity-check matrix and the transmit antenna for transmitting the codeword. More specifically, a condition of the parity-check matrix for achieving the maximum diversity varies according to whether the parity-check matrix is systematic, and according to the number of the transmit antennas. Accordingly, to achieve maximum diversity using an LDPC in a multiple antenna communication system, it is necessary to define the condition of the parity-check matrix and the distribution criterion of the codeword per transmit antenna.